The EKI algorithm we use is detailed in [1]}.
The algorithm iteratively updates an ensemble of parameters,
\(\mathbf {\theta }_m^{(n)}\) , where \(m=1,\dots M\)  denotes an ensemble member, and the
superscript \(n\)  denotes the iteration count. The algorithm uses the ensemble to update
parameters according to the following equation
\(\mathbf {\theta }_{m}^{(n+1)} = \mathbf {\theta }_{m}^{(n)} + C_{\mathbf {\theta } \mathcal {G}}^{(n)}\left( \Gamma + C_{\mathcal {G}\mathcal {G}}^{(n)}\right)^{-1}\left(\mathbf {y} - \mathcal {G}_T(\mathbf {\theta }_{m}^{(n)})\right)\,,\) 
